VẬT lý địa CHẤN 13 deco

n In Fourier domain: Cross-correlation = Multiplication of Amplitude spectrum and Subtraction of Phase spectrum... Autocorrelation functions contain reverberationsa A gradually decaying

x i : (i=0 n)

y i : (i= 0 n)

In Fourier domain:

Cross-correlation = Multiplication of Amplitude spectrum

and Subtraction of Phase spectrum

Reynolds, 1997

Cross-correlation function

τ

Auto-correlation of two identical waveforms

xx

xx norm

φ ;

yy xx

xy norm

Auto-correlation: multiples

Autocorrelation functions contain reverberations

a) A gradually decaying function indicative of short-period

reverberation

b) A function with separate side lobes indicative of long-period

reverberations: multiples

Filter Operator

Input function Output function

General Filter

Filter Operator

Deltafunction Impulse response

General Filter

Example of input response

From geology to seismogram

y(t) = g(t) ∗ f(t)

Filterfunction

Convolution

Inputfunction outputfunction

Convolution

Seismic trace Source wavelet Reflectivity function

k = 0 m+n

g i = (i=0 m)

f j = (j= 0 n)

In Fourier domain:

Convolution = Multiplication (of Amplitudes

and Addition of Phasespectrum)

Numerical implementation of convolution

y

0

g t = kδ t ∗ s t ∗ n t ∗ p t ∗ e t + Noise

Impulse

of source

Near-surface zone of source

Additional modifying Effects (absorption, wave conversion)

=

=

Principle of Wiener filtering

Input-Function ∗ Filter = Output-Function

(known) (wanted) (known)

Common shot-gathers just after demultiplexing

Corrected for wavefront divergence After trace balancing

Yilmaz, 1987

After spiking deconvolution

Undeconvolved gather: reverberating wavetrainsDeconvolved gather: note the prominent reflections

Undeconvolved gathers Deconvolved gathers

After

Deconvolution

After

Deconvolution